Refer to the following frequency distribution for Questions 1, 2, 3, and 4.
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The frequency distribution below shows the distribution for suspended solid concentration (in ppm) in river water of 50 different waters collected in September 2012. Concentration (ppm)
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Frequency
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20 - 29
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1
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30 - 39
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7
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40 - 49
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8
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50 - 59
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11
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60 - 69
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11
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70 - 79
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7
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80 - 89
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3
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90 - 99
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2
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1. What percentage of the rivers had suspended solid concentration less than 40?
2. Calculate the mean of this frequency distribution.
3. In what class interval must the median lie? Explain your answer. (You don't have to find the median)
4. Assume that the largest observation in this dataset is 98. Suppose this observation were incorrectly recorded as 988 instead of 98. Will the mean increase, decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers.
Refer to the following information for Questions 5 and 6.
A coin is flipped three times. Let A be the event that the outcome of the first flip is a heads. Let B be the event that the outcomes of second and third flips are both tails..
5. What is the probability that the outcomes of the second and third flips are both tails, given that the first one is a heads? (10 pts)
6. Are A and B independent? Why or why not?
A random sample of song playing times in seconds is as follows:
231 220 213 230 293
7. Find the standard deviation.
8. Are any of these playing times considered unusual in the sense of our textbook? Explain. Does this differ with your intuition? Explain.
Refer to the following situation for Questions 9, 10, and 11.
The five-number summary below shows the grade distribution of two STAT 200 quizzes.
For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case.
9. Which quiz has greater interquartile range in grade distribution?
10. Which quiz has the greater percentage of students with grades 80 and over?
11. Which quiz has a greater percentage of students with grades less than 60?
12. A random sample of 225 SAT scores has a mean of 1522. Assume that SAT scores have a population standard deviation of 300. Construct a 95% confidence interval estimate of the mean SAT scores. Refer to the following situation for Questions 9, 10, and 11.
Refer to the following information for Questions 13 and 14.
There are 1000 students in the senior class at a certain high school. The high school offers two Advanced Placement math / stat classes to seniors only: AP Calculus and AP Statistics. The roster of the Calculus class shows 95 people; the roster of the Statistics class shows 86 people. There are 43 overachieving seniors on both rosters.
13. What is the probability that a randomly selected senior is in exactly one of the two classes (but not both)? (10 pts)
14. If the student is in the Calculus class, what is the probability the student is also in the Statistics class? (10 pts)
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Minimum
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Q1
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Median
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Q3
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Maximum
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Quiz 1
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12
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40
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60
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95
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100
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Quiz 2
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20
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35
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50
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80
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100
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A box contains 5 chips. The chips are numbered 1 through 5. Otherwise, the chips are identical. From this box, we draw one chip at random, and record its value. We then put the chip back in the box. We repeat this process two more times, making three draws in all from this box.
15. How many elements are in the sample space of this experiment?
16. What is the probability that the three numbers drawn are all different?
17. What is the probability that the three numbers drawn are all odd numbers?
Questions 18 and 19 involve the random variable x with probability distribution given below
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. x
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2
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3
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4
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5
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10
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()Px
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0.1
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0.2
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0.3
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0.2
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0.2
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18. Determine the expected value of x.
19. Determine the standard deviation of x.
Consider the following situation for Questions 20 and 21.
Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Capital Air is a small commuter airline. Its past records indicate that 85% of the people who make a reservation will show up for the flight. The other 15% do not show up. Capital Air decided to book 11 people for today's flight. Today's flight has just 10 seats.
20. Find the probability that there are enough seats for all the passengers who show up. (Hint: Find the probability that in 11 people, 10 or less show up.)
21. How many passengers are expected to show up?
22. Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3, we perform the following hypothesis test.
0:750Hμ=
1:750Hμ<
What is the conclusion of the test at the level? Explain your answer. (20 pts) 0.10α=
Refer to the following information for Questions 23, 24, and 25.
The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
23. What is the probability that a randomly person has an IQ between 85 and 115?
24. Find the 90th percentile of the IQ distribution.
25. If a random sample of 100 people is selected, what is the standard deviation of the sample mean?
26. Consider the hypothesis test given by
01:530:530.HHμμ=≠
In a random sample of 81 subjects, the sample mean is found to be Also, the population standard deviation is 524.x=27.σ=
Determine the P-value for this test. Is there sufficient evidence to justify the rejection of at the level? Explain. (20 pts) 0H 0.01α=
27. A certain researcher thinks that the proportion of women who say that the earth is getting warmer is greater than the proportion of men.
In a random sample of 250 women, 70% said that the earth is getting warmer.
In a random sample of 220 men, 68% said that the earth is getting warmer.
At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer?
Show all work an
data for Questions 28 and 29.
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x
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0
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- 1
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1
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2
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3
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y
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2
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- 2
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5
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4
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7
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30. The UMUC Daily News reported that the color distribution for plain M&M's was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M's was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer.
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Color
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Brown
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Yellow
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Orange
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Green
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Tan
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Number
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45
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13
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17
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7
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18
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Refer to the following data for Questions 28 and 29.
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: x
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0
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- 1
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1
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2
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3
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y
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2
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- 2
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5
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4
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7
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